As a member of the Laughlin series, the \(\nu =1/2\)  Laughlin state has a TEE of \(\log \sqrt{2}\) , which can be extracted as a thermodynamic entropy change in a QPC. The associated entropy crossover can be obtained exactly from the TBA free energy, as shown in Fig. 1 in the main text. Interestingly, this case can also be mapped to free fermions [1]}, [2]}, [3]}, yielding an analytically exactly solvable model, and the resulting TEE can be associated with a free Majorana fermion.
